June 30, 2011 • 24 mins
Whether it's Art Garfunkel's mathematics degree or the structure of the chromatic scale, it's easy to correlate music and math. But why are so many musical minds also well suited for number crunching? Tune in to learn more about music and math.
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Episode Transcript
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Speaker 1 (00:03):
Welcome to Stuff to Blow your Mind from how Stuff
Works dot com. Hey, welcome to Stuff to Blow your Mind.
My name is Robert Lamb, and I'm Julie Douglas. And
you know, Julie, neither of us are really math people.
It's like we don't do a lot of recreational math. Yeah,
(00:24):
and we know. I'm a math folk. I just started
to same math and I started to get sweaty palms. Yeah.
Um and uh, but but but but we both enjoy music,
different types of music, I think. I mean there's some crossover.
It's not you know, it's kind of like a ven
diagram I would imagined. But um, see there you go
with the math. Yeah goodness, yeah, goodness me because this
(00:45):
is exactly what we're talking about. Math and music, um,
kind of lining up with each other, um, describing each other.
And we end up with this this idea in our head,
especially uh, those of us who are not math people
and enjoy music but don't have musical training per se um.
We end up looking back at it where we see
(01:07):
mathematicians who are really good at music or musicians that
have mathematical background, and we start saying, WHOA, what's going
on here? This seems to be the case, right right,
And I think you made the great analogy yesterday, like, oh, actors,
yeah crazy, all actors are crazy. Right. It's like if
you if you don't have an acting background, you don't
know many actors, you're not crazy. You don't know many
(01:27):
crazy people. You see crazy actors, and it's easy to
make that generality that, wow, they must be All actors
must be crazy, and their craziness must make them great actors.
Or maybe their acting makes them great crazies. I don't know. Yeah, yeah,
it's the that's the dog wagon the tail there. Um.
So yeah, we're going to try to look at this
idea of math and music being intertwined in perhaps being
(01:49):
inherent and um, and we'll try to see if there
really is a correlation between mathematics and musicians. Yeah. Now,
just to start off, like some famous mathematicians and slash
musicians or famous musicianstead have mathematical background. Um. One one hand,
we have Einstein himself, who was a violinist. Yeah. Um,
(02:10):
Brian May of Queen was an astrophysicist, um, which I've
always found kind of interesting. I don't know if it
really I haven't listened to queen in a long time,
but I don't remember there being much astrophysics UM injected
into the song. Yeah, maybe it was all happening just
with the music, just with the guitars, you know, because
(02:30):
and he he has returned to this discipline. Yes, yeah, yeah, yes, yeah,
there have been some interesting articles about it in recent years. UM.
Then we have people like Dan Snaith a k a
Caribou who has a mathematics background, though I've seen interviews
where he's very dismissive of the idea that there's any
really connectivity between the two. I think it was like
(02:51):
a was it an interview on data transmission? I can't
remember me it was linked to on data transmission UM
that code out UK where someone asked him about in
Cariboo was like you know math, yeah, math, math, different things.
So it's kind of disappointing. You can imagine the the interviewers,
you know, kind of slumping down, you know when he
(03:11):
got that answer. But other ones are Garfuncle had a
master's degree in mathematics, which I was not aware of.
I wasn't. I was surprised by that one. Yeah, I mean,
certainly his hair seems to indicate some sort of like
science lab type situation. But but no, he and again
I can't think of any Garfuncle songs where where I
have listened to him and be like, wow, bright Eyes
(03:32):
is such a mathematical song, you know. And again maybe
I'm I'm missing the finer corners of his discography, but yeah, um.
And then another one that comes to mind, uh is
a chat by the name of Rupert Way, who DJ
is under the name dj Irk. Yeah, and I actually
interviewed him for the blogs a little while back, and uh,
(03:53):
he has like a PhD in uh, some kind of
type of mathematics that dynamic systems something. It kind of
it just goes right over my head when when he
told me what it was. But but yeah, And there're
just a few there. Do you have any that I'm
leaving off? No, No, that that sounds Um, those are
some of the big ones, I think. And I was
I was actually revisiting your interview with him, and he
(04:15):
was talking. You were asking him about the connection between
Mathew music and I think he was saying that he
doesn't it doesn't really help anymore than it does with
what he says, say around trip a trip around the supermarket.
I've obviously taken that out of context. Uh, but he
did say something about mental agility, good memory, good numerous
(04:39):
e and a lot of determination, he says, or what
really counts. And although these are math related I'm quoting him,
they are not math specific. There are lots of overriding
instinctive and emotional factors too, which I thought was interesting
because he's he's sort of saying, yeah, all of this helps,
but it does not make you a musician per se,
(05:00):
because there are some factors that you just can't that
don't fit into the mathematical model, so to speak. Right. Yeah,
his answer was far more insightful than caribous. Yeah, yeah, yeah,
he actually he went on to say some very interesting stuff. Actually,
So if you haven't checked out Robert's blog on that
with with dj Oric, should definitely check that out. Yeah yeah,
I'll throw the link up. But but yeah, you end
(05:21):
up in the in this this situation where the the
answer is kind of yeah, kind of yeah, but also
not really um and and there's no real firm answer
because I mean, when you break it down, UM, I
mean we we've discussed in the past, like mathematics, what
is it is the human invention that just is so
clever that it describes everything in the universe? Or is
(05:44):
it a discovery? Did we find the secret language of
the universe and we're so awesome because we found it? Again,
humans end up looking pretty awesome. Either way, you spend
that but if but but but either way, you're talking
about a system of numbers that can describe everything. So
it stands to reason that it would be able to
describe music, right, Right, And yes, so there are definitely
(06:07):
some similarities with that because you would ask the same
thing about music in a sense, right, it is music
something that we discovered is just sort of inherent in
in us. And then we've talked about even our fingers before, Right,
we've got five fingers on each hand, and how that's
determined our currency in the way that we count in
number systems, and same thing with music. It's it's determined
the way that we have, Uh, created scales, and we
(06:29):
created instruments. Yeah, like strings vibrated a certain frequency and
you can measure those mathematically. Sound waves can also be
described by mathematical equations. Uh. I mean it comes down
to like scientists of any discipline, they use mathematics to
describe the physical world. Changing physical world of movable opjects,
and they predict the outcome of physical process, so you
(06:54):
know there's gonna be some cross over there. But then again,
an equation is not going to be able to describ
have a piece of music, and uh, I mean there
are a certain mathematical well, well you can there are
equations that can describe some of the mathematical structures that
are inherent in music, but you're not going to be
able to like to say, um, yeah, I want to
(07:14):
listen to that. Um, you know that can concerto by
so and so, But I don't have time for the
full thing. Just send me the equation. Well, and it's
interesting too, because the each equation you could interpret in
a different way as a musician, right yeah. But I
mean so there's that's the part of it that's like, well, okay,
here's here's the precise language. Um that you know, and
(07:37):
again drawing parallels to math, Math has a universal precise language. Right.
But once you know, you give this equation of music
to someone, they might perform it in a completely different
way or take liberties with it that you wouldn't necessarily
see in math. But again again talking about similarities, Um,
both disciplines gravitate towards symmetry. Right. You see this in
(08:00):
music all the time. Um, of course there's there's cacophony, right,
Uh yeah, noise music and all that. I mean that's
the thing too. It's like music when you're talking about
like what is music? Yeah, there's some there are there
certain types of music that are very mathematical sounding, and
you can break down you can you know, apply some
some number to the numbers to the music theory of
it all, and it makes perfect sense. But then you
(08:22):
pull out some sort of like noise artist where they're
using very abstract sounds music that uh, to quote my wife,
sounds like someone through a xylophone down a stairwell. And
then it's gonna be hard to say like, oh, well, mathematically,
this is what's going on there. But then again, you
could also make the counter argument that even a chaotic system, um,
there's math going on there. Can you can go back
(08:45):
and forth. And now the ancient Greeks they definitely thought
there was there were numbers tied up in music, that
math and music were very closely related. Is this uh
pithe Pythi versus yeah, yeah, yeah, like because he use
all about the ratio of yeah, yeah, and his his
whole like system of of education. Um. They considered music
(09:05):
to be a strictly mathematical disciple in involving number of relationships,
ratios and proportions, and so if you break it down,
it would basically be a subdivision to quantitative mathematics in
Pithagorean time. So yeah, harmonica ratios proportions central in the
Greek's understanding too musical, okay, yeah, And so just to
(09:26):
back up a little bit to the five tone or
the pentatonic scale developed about three thousand years ago in China,
and then the Greeks they have the seven tone scale, right, um.
And then then we're talking about the twelve tone scale, right,
And this is when we're talking about Pythagora is really
obsessing on these ratios. And I won't go into the
math behind it, but that's how we sort of came
(09:46):
up with these varying skills. And it wasn't till around
I think Box time where they took one of those
ratios that was a bit off and and tinkered with
it and they came up with the final twelve tones. Um.
So again there's there's a system behind there. There's math
that's driving the way that we are expressing music, which
(10:07):
is pretty interesting, all right, But what exactly is going
on in the brain? Right? Yes? Yes, so let's uh,
let's take a quick break, and when we come back,
we will look at math and music in the human mind.
This presentation is brought to you by Intel sponsors of tomorrow,
(10:32):
and we're back music brains. What's happened? Yes, um, so,
obviously scientists have looked at the brain and analyze what
exactly is going on when we think about music or
contemplate music versus contemplating math, and they have Scientists actually
(10:52):
looked at brain injuries that suggest a single region in
the left hemisphere of the brain gives rise to sequential
analytic processing, which is used for both doing algebra and
reading music. All right, But then on the other hand,
there was a two thousand eight study from the University
of Arkansas that used a human Information Processing Survey instrument
or a HIPS instrument to measure hemispheric collaterality. They used
(11:16):
a hundred and one participants asked them to discuss their
prowess in first math and then in music, and their
finding suggested that math is a left hemisphere preference and
music is a right hemisphere preference. Okay, well, it's interesting,
right because we've talked about music before and how it
affects the brain, and we've found that there is no
one music center, um, so it's sort of spread up
(11:38):
throughout the brain. But to to know that's obviously engaging
in a part of the brain that is that's tracking
um math is interesting. And likewise, there have been a
number of studies which sort of say different things about
exactly how musical education affects one's mathematical prowess. Um. They
have been studies they've found that people with musical training
(11:59):
outperform people who don't have musical training. Um. But then
there's uh, there's stuff like for instance, there was the
Montreal Montreal Piano Project. All right, half the children were
giving piano lessons for three years, and after two years,
the piano playing kids were outscoring the others on spatial ability.
So the argument here was that yeah, learning music helps you,
(12:20):
um helps you with math because it's reinforcing the brain
circuits that power spatial thinking, which comes in handy not
only for knowing what keys match up with what note,
but also in geometry, physics, and chemistry, all right, But
then opposing that we have um um a study from
the University of Toronto. Uh, and this one, this one
(12:41):
was pretty cool too. They took six year olds, all right,
and they took weekly piano and singing lessons throughout the
school year, and they exhibited an average i Q increase
of seven h point zero points. Right. The other six
year olds who took either weekly drama lessons or received
no extra trick curricular lessons displayed an average i Q
(13:02):
rise of four point three points. So that's another one
that also seems to indicate, all right, they're they're learning
music and this is helping them with their scores. But
I also think, like non scientifically, that maybe the drama
kids were just having more fun and didn't have as
much time to really play with the studying all that much. Huh,
all right, yeah, they were too busy emoting. And then
(13:24):
the kids who didn't get anything, they were just setting
around in study hall like destroying desks with tiny axes
or something. They weren't having new experiences. And we just
talked about this so important is that you need to
to have new experiences in order to create new pathways. Yeah,
discussed in our Einstein's Brain podcasts. Alright, so there's there's
some basis here for some some waltzing, let's say, between
(13:48):
between the brain and music and maths. What I was
interested in knowing was whether anybody had ever actually taken
a piece of music and said, okay, here's here's here's
some math right here, right, because there are certain pieces
of music that I hear sometimes and I'm like, god,
I can I can't. Maybe geometrically, I can see things
going on in this music, um, which is sort of
(14:10):
interesting way you're talking about in your mind, not the
not the visualizer that pops up, yeah, exactly, not in
front of my computer with you know, I don't have
like purple splashes. Um. But what I found was that
there is a book called meta Magical Femus. It's called
Questing for the Essence of Mind and Pattern by Douglas
host Daughter And he actually looked at Chopin's music and
(14:32):
box as well, but he said, Chapon's music is filled
to the brim that I'm quoting with algebra algebraic tricks
of cross rhythm. A famous example is in his iconoclastic
waltz Opus forty two in a flat major written eighteen
forty and this waltz. The baseline follows the usual oompapa
convention of the waltz. I don't know if papa, yeah nice, yeah, okay, okay,
(14:57):
But the melody of the first section completely counters this
three nuts. It's six six eighth notes. Instead of being
broken up into three pairs aligned with the left hand
bounces while playing form two triplets. The initial notes of
the success of triplets are to be clearly emphasized and prolonged,
thus creating a higher level melody abstracted out of the
quietly rippling right hand. Yeah. I think I'm gonna have
(15:20):
to hear an example and put that together. Yes, yes,
And he's saying that this melody is composed of two
notes per measure beating regularly against three notes of a
waltzing base. And he says it's a marvelous trump let
aier effect, which which means the oral equivalent to an
optical illusion. Basically, So let's take a quick listen to
uh this waltz. It was forty two in a flat major.
(15:53):
I don't know, did you hear it? Um? Yeah, I
think I can. I can get a sense of some
of that coming together. I definitely got the oom Papa. Yes.
So that's one example where someone has actually tried to
map this, which is kind of interesting. And um. There
was another example that I found by mathematician Hence Strob,
(16:14):
and he talks about modal jazz. And the reason I
really wanted to look into this is because jazz modal
jazz is uh is someone like uh, it was like
Miles Davis. Miles Davis is usually attributed to be the
person that that sort of creative medal jazz are popularized
it um, particularly in the fifties. So this modal jazz
(16:36):
is is said to have a more horizontal structure, whereas
traditional jazz is structured more vertically, and modal just means
that he took a bunch of notes and he sort
of squished them all in this my my horrible understanding
of both mathematics and UM and music theory. Um. So
it just seems weird that jazz would like I thought
jazz was free flowing, man. I thought you can't put
(16:59):
math on jazz. Jazz as its own rhythm. Yeah, well
that's the incredible thing. And that's why I love Miles
Davis is because it does seem like there's a lot
of um sort of off off the cuff playing, right,
But I mean, the fact of the matter is is
that they're taking some some very um concentric like rhythms
(17:19):
and then they're playing off of that. So what you
might hear which sounds sort of like, oh wow, man,
that that cat is just going nuts on the saxophone, Um,
they are, but but they're doing it in the sort
of loops, um, these horizontal loops, and they're not doing
a lot of key changes. So let me try tokay. So, like,
if you had like a really crazy story that that
that at its heart followed a traditional story arc, even
(17:42):
if it involved like art arts from Mars in love
with each other or something. Yeah, yeah, And everybody knows
that that once you start, you know, to be good
at any craft, right, you have to know the absolute basics.
You have to master it. And um, you know, Myles
Savis is someone who certainly was master at what he did,
So that gave him the othery to sort of riff
off of stuff and um, play with modal notes and
(18:04):
and do all these sort of different things that actually
changed people's perception of that music itself. So what I
thought was interesting about it is that this this guy Hendstrub,
he talks about the traditional jazz being structured more vertically,
which means in this context that traditional jazz impro improvisations
are based on chord progressions and modal jazz. On the
other hand, improvised improvisations typically go on for long periods
(18:28):
without any chord change. So that so I was talking
about earlier, and the interest is more turned towards the
melodic line. Uh So, it's it's a That's why I
thought it was sort of interesting to me because I
thought I can see that visually. I can see that
in Miles Davis's music. You can see this horizontal spreading.
You can see in Yo yo mom when he does
uh the box suitets um. You can see it maybe
(18:50):
even in like PJ. Harvey and like White Chalk, like
the Cults an album that has sort of like this
horizontal spreading, although you could say there are some there's
some vertical loops of coophany in that as well. But anyway,
let's let's just listen to a quick clip from kind
of Blue Miles Davis. Cool. Yeah, Now, did you say
(19:21):
this is actually your favorite track, your favorite song, favorite album?
I mean the entire album is my favorite. There's actually
not one song on there that I would say that
is my absolute favorite. I love it as a whole piece,
and um, you know we've talked about this before and
getting in the zone, and um, this is one of
those pieces of music that I can listen to and
it does sound it kind of put me into a
(19:43):
different state that allows me to think clearer, think at
higher levels. I think, is why I like it. And
also we've talked about this too, like lyrics sometimes bother
me when I'm trying to cogitate up in Monogaen. So
you know, that's that's that's some of the discovery here
where we're seeing that the music and the math, at
least again geometrically, I can see it. I don't know
(20:04):
if it's the same for other people. But there's a
guy named Dave Russ, and he's associate professor of mathematics
at Northern Illinois University, and he really does try to
make this correlation between music and math, and he thinks
it's important for for students to better understand math. In fact, well,
he says mathematics, like music, embodies certain patterns and ideas
(20:24):
which don't translate well into words, as we found out. Uh,
as you listener, hath end up. We can feel them,
see them, understand them, but only after we have really
worked to lift them off the paper and into our minds,
only after we've tried to see where they come from,
only after considerable practice with the minutia, gradually adding the trills. Uh,
(20:47):
do we have the full spirit of the idea? Mathematics
like music as a human adventure, people create and discover it,
they try to then share it and enjoy it. Yeah.
I mean I I definitely found that to be the
case with both music and mathematics, because on one hand,
I love um certain genres of music, and I'll you know,
I'll listen to it all the time, but I'm not
(21:07):
necessarily really good at describing what's great about it. Like
if if I'm like, you know, talking to a friend,
I'm like, oh, you gotta listen to this new mix
by so and so, and they might be like, well,
what's awesome about it? And I may be a little
stump for words, you know, unless I have some time
to prep. Likewise, with mathematics, I was the last week
I was working on an article about number theory and
like number theory. Especially when writing for a general audience
(21:30):
and a you know, non math audience, it's it quickly
becomes a conversation that cannot be really held in English
but needs to be held or any language, but needs
to be held in math. You know, it needs to
be held with numerals and and equations. So it becomes
increasingly difficult to to explain the topic without being the
(21:51):
topic right right. And that's why us wildly humans, I suppose,
turned to math and music to try to express ourselves
and our ideas and in a better way. Yeah, because
I think I saw it pointed out that both both
music and math are like they're self describing things. The
music describes itself, the math describes itself, and h and yeah,
at the at the end of the day, it kind
(22:11):
of sounds like, you know, defeatist, but they both kind
of described themselves the best. There we go looking in
the mirror. I'm trying to change the world. I don't
know I was trying to do, Michael Jackson, there apologize
you were trying to do like an impersonation. I was
thinking that math and music we're looking at each other
in the world. And then excuse me, looking at each
(22:33):
other in the mirror, and then I started thinking about
that song man in the mirror. Oh, it's just bad
all around. No, No, it wasn't that bad. It was good.
You did fun um. If we have the speaking of math,
we have a listener mail here, a listener by the
name of Timothy. He says, hello, stuff to all your
mind crew. I just wanted to say thank you for
the unusually deep mathematics podcast. I am a science and
(22:54):
philosophy enthusiast, and I just happened to be in the
middle of a book called A World Without Time, the
Forgotten Legacy of Godal and Einstein when you aired your podcast.
I personally believe that Godal's incompleteness, theorems, the existence of
non eucludean geometries, the necessity of imaginary numbers, and such
all point to math is a formal system invented by humans.
(23:15):
It strikes me as something similar to a game like chess,
where simple rules give rise to an incredibly complex overall system.
I could imagine a chess like game being created to
model physics. What is interesting to me is that Godal,
like many mathematicians, was of the opposite persuasion. He believed
that math exists independent of the human mind. By the way,
(23:36):
one of my favorite books is also godal escher Bach
by Douglas hofstadtur Hofstadter Yeah, can we as ye, which
I highly recommend it to any listeners who also enjoyed
the Math podcast. Thank you for all the hard work
you to do, Tim. Thanks Tim. Yeah, so, yeah, the
we have the podcast that we've in referenced earlier. Um
(23:59):
is math a human invention or a human discovery? And uh, yeah,
that was a lot of fun to do. Yeah it was.
And and uh again, we were both a little bit
trepidacious about, you know, entering into the realm of math,
but it turns out it was not painful at all. Yeah,
And if you want to enter into our realm, then
all you have to do is check out Facebook and Twitter.
It is not painful either, not painful at all. I
(24:21):
mean unless like twitters down or something, and it can
be a little frustrating. But now we'll blow the mind
on both of those and we update that with all
sorts of links to cool stuff. We're reading cool stuff,
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we would love to hear from you. So Please feel
free to drop us a line at blow the Mind
at how stuff works dot com. Be sure to check
(24:44):
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how Stuff Work staff as we explore the most promising
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Welcome to Stuff to Blow your Mind from how Stuff
Works dot com. Hey, welcome to Stuff to Blow your Mind.
My name is Robert Lamb, and I'm Julie Douglas. And
you know, Julie, neither of us are really math people.
It's like we don't do a lot of recreational math. Yeah,
(00:24):
and we know. I'm a math folk. I just started
to same math and I started to get sweaty palms. Yeah.
Um and uh, but but but but we both enjoy music,
different types of music, I think. I mean there's some crossover.
It's not you know, it's kind of like a ven
diagram I would imagined. But um, see there you go
with the math. Yeah goodness, yeah, goodness me because this
(00:45):
is exactly what we're talking about. Math and music, um,
kind of lining up with each other, um, describing each other.
And we end up with this this idea in our head,
especially uh, those of us who are not math people
and enjoy music but don't have musical training per se um.
We end up looking back at it where we see
(01:07):
mathematicians who are really good at music or musicians that
have mathematical background, and we start saying, WHOA, what's going
on here? This seems to be the case, right right,
And I think you made the great analogy yesterday, like, oh, actors,
yeah crazy, all actors are crazy. Right. It's like if
you if you don't have an acting background, you don't
know many actors, you're not crazy. You don't know many
(01:27):
crazy people. You see crazy actors, and it's easy to
make that generality that, wow, they must be All actors
must be crazy, and their craziness must make them great actors.
Or maybe their acting makes them great crazies. I don't know. Yeah, yeah,
it's the that's the dog wagon the tail there. Um.
So yeah, we're going to try to look at this
idea of math and music being intertwined in perhaps being
(01:49):
inherent and um, and we'll try to see if there
really is a correlation between mathematics and musicians. Yeah. Now,
just to start off, like some famous mathematicians and slash
musicians or famous musicianstead have mathematical background. Um. One one hand,
we have Einstein himself, who was a violinist. Yeah. Um,
(02:10):
Brian May of Queen was an astrophysicist, um, which I've
always found kind of interesting. I don't know if it
really I haven't listened to queen in a long time,
but I don't remember there being much astrophysics UM injected
into the song. Yeah, maybe it was all happening just
with the music, just with the guitars, you know, because
(02:30):
and he he has returned to this discipline. Yes, yeah, yeah, yes, yeah,
there have been some interesting articles about it in recent years. UM.
Then we have people like Dan Snaith a k a
Caribou who has a mathematics background, though I've seen interviews
where he's very dismissive of the idea that there's any
really connectivity between the two. I think it was like
(02:51):
a was it an interview on data transmission? I can't
remember me it was linked to on data transmission UM
that code out UK where someone asked him about in
Cariboo was like you know math, yeah, math, math, different things.
So it's kind of disappointing. You can imagine the the interviewers,
you know, kind of slumping down, you know when he
(03:11):
got that answer. But other ones are Garfuncle had a
master's degree in mathematics, which I was not aware of.
I wasn't. I was surprised by that one. Yeah, I mean,
certainly his hair seems to indicate some sort of like
science lab type situation. But but no, he and again
I can't think of any Garfuncle songs where where I
have listened to him and be like, wow, bright Eyes
(03:32):
is such a mathematical song, you know. And again maybe
I'm I'm missing the finer corners of his discography, but yeah, um.
And then another one that comes to mind, uh is
a chat by the name of Rupert Way, who DJ
is under the name dj Irk. Yeah, and I actually
interviewed him for the blogs a little while back, and uh,
(03:53):
he has like a PhD in uh, some kind of
type of mathematics that dynamic systems something. It kind of
it just goes right over my head when when he
told me what it was. But but yeah, And there're
just a few there. Do you have any that I'm
leaving off? No, No, that that sounds Um, those are
some of the big ones, I think. And I was
I was actually revisiting your interview with him, and he
(04:15):
was talking. You were asking him about the connection between
Mathew music and I think he was saying that he
doesn't it doesn't really help anymore than it does with
what he says, say around trip a trip around the supermarket.
I've obviously taken that out of context. Uh, but he
did say something about mental agility, good memory, good numerous
(04:39):
e and a lot of determination, he says, or what
really counts. And although these are math related I'm quoting him,
they are not math specific. There are lots of overriding
instinctive and emotional factors too, which I thought was interesting
because he's he's sort of saying, yeah, all of this helps,
but it does not make you a musician per se,
(05:00):
because there are some factors that you just can't that
don't fit into the mathematical model, so to speak. Right. Yeah,
his answer was far more insightful than caribous. Yeah, yeah, yeah,
he actually he went on to say some very interesting stuff. Actually,
So if you haven't checked out Robert's blog on that
with with dj Oric, should definitely check that out. Yeah yeah,
I'll throw the link up. But but yeah, you end
(05:21):
up in the in this this situation where the the
answer is kind of yeah, kind of yeah, but also
not really um and and there's no real firm answer
because I mean, when you break it down, UM, I
mean we we've discussed in the past, like mathematics, what
is it is the human invention that just is so
clever that it describes everything in the universe? Or is
(05:44):
it a discovery? Did we find the secret language of
the universe and we're so awesome because we found it? Again,
humans end up looking pretty awesome. Either way, you spend
that but if but but but either way, you're talking
about a system of numbers that can describe everything. So
it stands to reason that it would be able to
describe music, right, Right, And yes, so there are definitely
(06:07):
some similarities with that because you would ask the same
thing about music in a sense, right, it is music
something that we discovered is just sort of inherent in
in us. And then we've talked about even our fingers before, Right,
we've got five fingers on each hand, and how that's
determined our currency in the way that we count in
number systems, and same thing with music. It's it's determined
the way that we have, Uh, created scales, and we
(06:29):
created instruments. Yeah, like strings vibrated a certain frequency and
you can measure those mathematically. Sound waves can also be
described by mathematical equations. Uh. I mean it comes down
to like scientists of any discipline, they use mathematics to
describe the physical world. Changing physical world of movable opjects,
and they predict the outcome of physical process, so you
(06:54):
know there's gonna be some cross over there. But then again,
an equation is not going to be able to describ
have a piece of music, and uh, I mean there
are a certain mathematical well, well you can there are
equations that can describe some of the mathematical structures that
are inherent in music, but you're not going to be
able to like to say, um, yeah, I want to
(07:14):
listen to that. Um, you know that can concerto by
so and so, But I don't have time for the
full thing. Just send me the equation. Well, and it's
interesting too, because the each equation you could interpret in
a different way as a musician, right yeah. But I
mean so there's that's the part of it that's like, well, okay,
here's here's the precise language. Um that you know, and
(07:37):
again drawing parallels to math, Math has a universal precise language. Right.
But once you know, you give this equation of music
to someone, they might perform it in a completely different
way or take liberties with it that you wouldn't necessarily
see in math. But again again talking about similarities, Um,
both disciplines gravitate towards symmetry. Right. You see this in
(08:00):
music all the time. Um, of course there's there's cacophony, right,
Uh yeah, noise music and all that. I mean that's
the thing too. It's like music when you're talking about
like what is music? Yeah, there's some there are there
certain types of music that are very mathematical sounding, and
you can break down you can you know, apply some
some number to the numbers to the music theory of
it all, and it makes perfect sense. But then you
(08:22):
pull out some sort of like noise artist where they're
using very abstract sounds music that uh, to quote my wife,
sounds like someone through a xylophone down a stairwell. And
then it's gonna be hard to say like, oh, well, mathematically,
this is what's going on there. But then again, you
could also make the counter argument that even a chaotic system, um,
there's math going on there. Can you can go back
(08:45):
and forth. And now the ancient Greeks they definitely thought
there was there were numbers tied up in music, that
math and music were very closely related. Is this uh
pithe Pythi versus yeah, yeah, yeah, like because he use
all about the ratio of yeah, yeah, and his his
whole like system of of education. Um. They considered music
(09:05):
to be a strictly mathematical disciple in involving number of relationships,
ratios and proportions, and so if you break it down,
it would basically be a subdivision to quantitative mathematics in
Pithagorean time. So yeah, harmonica ratios proportions central in the
Greek's understanding too musical, okay, yeah, And so just to
(09:26):
back up a little bit to the five tone or
the pentatonic scale developed about three thousand years ago in China,
and then the Greeks they have the seven tone scale, right, um.
And then then we're talking about the twelve tone scale, right,
And this is when we're talking about Pythagora is really
obsessing on these ratios. And I won't go into the
math behind it, but that's how we sort of came
(09:46):
up with these varying skills. And it wasn't till around
I think Box time where they took one of those
ratios that was a bit off and and tinkered with
it and they came up with the final twelve tones. Um.
So again there's there's a system behind there. There's math
that's driving the way that we are expressing music, which
(10:07):
is pretty interesting, all right, But what exactly is going
on in the brain? Right? Yes? Yes, so let's uh,
let's take a quick break, and when we come back,
we will look at math and music in the human mind.
This presentation is brought to you by Intel sponsors of tomorrow,
(10:32):
and we're back music brains. What's happened? Yes, um, so,
obviously scientists have looked at the brain and analyze what
exactly is going on when we think about music or
contemplate music versus contemplating math, and they have Scientists actually
(10:52):
looked at brain injuries that suggest a single region in
the left hemisphere of the brain gives rise to sequential
analytic processing, which is used for both doing algebra and
reading music. All right, But then on the other hand,
there was a two thousand eight study from the University
of Arkansas that used a human Information Processing Survey instrument
or a HIPS instrument to measure hemispheric collaterality. They used
(11:16):
a hundred and one participants asked them to discuss their
prowess in first math and then in music, and their
finding suggested that math is a left hemisphere preference and
music is a right hemisphere preference. Okay, well, it's interesting,
right because we've talked about music before and how it
affects the brain, and we've found that there is no
one music center, um, so it's sort of spread up
(11:38):
throughout the brain. But to to know that's obviously engaging
in a part of the brain that is that's tracking
um math is interesting. And likewise, there have been a
number of studies which sort of say different things about
exactly how musical education affects one's mathematical prowess. Um. They
have been studies they've found that people with musical training
(11:59):
outperform people who don't have musical training. Um. But then
there's uh, there's stuff like for instance, there was the
Montreal Montreal Piano Project. All right, half the children were
giving piano lessons for three years, and after two years,
the piano playing kids were outscoring the others on spatial ability.
So the argument here was that yeah, learning music helps you,
(12:20):
um helps you with math because it's reinforcing the brain
circuits that power spatial thinking, which comes in handy not
only for knowing what keys match up with what note,
but also in geometry, physics, and chemistry, all right, But
then opposing that we have um um a study from
the University of Toronto. Uh, and this one, this one
(12:41):
was pretty cool too. They took six year olds, all right,
and they took weekly piano and singing lessons throughout the
school year, and they exhibited an average i Q increase
of seven h point zero points. Right. The other six
year olds who took either weekly drama lessons or received
no extra trick curricular lessons displayed an average i Q
(13:02):
rise of four point three points. So that's another one
that also seems to indicate, all right, they're they're learning
music and this is helping them with their scores. But
I also think, like non scientifically, that maybe the drama
kids were just having more fun and didn't have as
much time to really play with the studying all that much. Huh,
all right, yeah, they were too busy emoting. And then
(13:24):
the kids who didn't get anything, they were just setting
around in study hall like destroying desks with tiny axes
or something. They weren't having new experiences. And we just
talked about this so important is that you need to
to have new experiences in order to create new pathways. Yeah,
discussed in our Einstein's Brain podcasts. Alright, so there's there's
some basis here for some some waltzing, let's say, between
(13:48):
between the brain and music and maths. What I was
interested in knowing was whether anybody had ever actually taken
a piece of music and said, okay, here's here's here's
some math right here, right, because there are certain pieces
of music that I hear sometimes and I'm like, god,
I can I can't. Maybe geometrically, I can see things
going on in this music, um, which is sort of
(14:10):
interesting way you're talking about in your mind, not the
not the visualizer that pops up, yeah, exactly, not in
front of my computer with you know, I don't have
like purple splashes. Um. But what I found was that
there is a book called meta Magical Femus. It's called
Questing for the Essence of Mind and Pattern by Douglas
host Daughter And he actually looked at Chopin's music and
(14:32):
box as well, but he said, Chapon's music is filled
to the brim that I'm quoting with algebra algebraic tricks
of cross rhythm. A famous example is in his iconoclastic
waltz Opus forty two in a flat major written eighteen
forty and this waltz. The baseline follows the usual oompapa
convention of the waltz. I don't know if papa, yeah nice, yeah, okay, okay,
(14:57):
But the melody of the first section completely counters this
three nuts. It's six six eighth notes. Instead of being
broken up into three pairs aligned with the left hand
bounces while playing form two triplets. The initial notes of
the success of triplets are to be clearly emphasized and prolonged,
thus creating a higher level melody abstracted out of the
quietly rippling right hand. Yeah. I think I'm gonna have
(15:20):
to hear an example and put that together. Yes, yes,
And he's saying that this melody is composed of two
notes per measure beating regularly against three notes of a
waltzing base. And he says it's a marvelous trump let
aier effect, which which means the oral equivalent to an
optical illusion. Basically, So let's take a quick listen to
uh this waltz. It was forty two in a flat major.
(15:53):
I don't know, did you hear it? Um? Yeah, I
think I can. I can get a sense of some
of that coming together. I definitely got the oom Papa. Yes.
So that's one example where someone has actually tried to
map this, which is kind of interesting. And um. There
was another example that I found by mathematician Hence Strob,
(16:14):
and he talks about modal jazz. And the reason I
really wanted to look into this is because jazz modal
jazz is uh is someone like uh, it was like
Miles Davis. Miles Davis is usually attributed to be the
person that that sort of creative medal jazz are popularized
it um, particularly in the fifties. So this modal jazz
(16:36):
is is said to have a more horizontal structure, whereas
traditional jazz is structured more vertically, and modal just means
that he took a bunch of notes and he sort
of squished them all in this my my horrible understanding
of both mathematics and UM and music theory. Um. So
it just seems weird that jazz would like I thought
jazz was free flowing, man. I thought you can't put
(16:59):
math on jazz. Jazz as its own rhythm. Yeah, well
that's the incredible thing. And that's why I love Miles
Davis is because it does seem like there's a lot
of um sort of off off the cuff playing, right,
But I mean, the fact of the matter is is
that they're taking some some very um concentric like rhythms
(17:19):
and then they're playing off of that. So what you
might hear which sounds sort of like, oh wow, man,
that that cat is just going nuts on the saxophone, Um,
they are, but but they're doing it in the sort
of loops, um, these horizontal loops, and they're not doing
a lot of key changes. So let me try tokay. So, like,
if you had like a really crazy story that that
that at its heart followed a traditional story arc, even
(17:42):
if it involved like art arts from Mars in love
with each other or something. Yeah, yeah, And everybody knows
that that once you start, you know, to be good
at any craft, right, you have to know the absolute basics.
You have to master it. And um, you know, Myles
Savis is someone who certainly was master at what he did,
So that gave him the othery to sort of riff
off of stuff and um, play with modal notes and
(18:04):
and do all these sort of different things that actually
changed people's perception of that music itself. So what I
thought was interesting about it is that this this guy Hendstrub,
he talks about the traditional jazz being structured more vertically,
which means in this context that traditional jazz impro improvisations
are based on chord progressions and modal jazz. On the
other hand, improvised improvisations typically go on for long periods
(18:28):
without any chord change. So that so I was talking
about earlier, and the interest is more turned towards the
melodic line. Uh So, it's it's a That's why I
thought it was sort of interesting to me because I
thought I can see that visually. I can see that
in Miles Davis's music. You can see this horizontal spreading.
You can see in Yo yo mom when he does
uh the box suitets um. You can see it maybe
(18:50):
even in like PJ. Harvey and like White Chalk, like
the Cults an album that has sort of like this
horizontal spreading, although you could say there are some there's
some vertical loops of coophany in that as well. But anyway,
let's let's just listen to a quick clip from kind
of Blue Miles Davis. Cool. Yeah, Now, did you say
(19:21):
this is actually your favorite track, your favorite song, favorite album?
I mean the entire album is my favorite. There's actually
not one song on there that I would say that
is my absolute favorite. I love it as a whole piece,
and um, you know we've talked about this before and
getting in the zone, and um, this is one of
those pieces of music that I can listen to and
it does sound it kind of put me into a
(19:43):
different state that allows me to think clearer, think at
higher levels. I think, is why I like it. And
also we've talked about this too, like lyrics sometimes bother
me when I'm trying to cogitate up in Monogaen. So
you know, that's that's that's some of the discovery here
where we're seeing that the music and the math, at
least again geometrically, I can see it. I don't know
(20:04):
if it's the same for other people. But there's a
guy named Dave Russ, and he's associate professor of mathematics
at Northern Illinois University, and he really does try to
make this correlation between music and math, and he thinks
it's important for for students to better understand math. In fact, well,
he says mathematics, like music, embodies certain patterns and ideas
(20:24):
which don't translate well into words, as we found out. Uh,
as you listener, hath end up. We can feel them,
see them, understand them, but only after we have really
worked to lift them off the paper and into our minds,
only after we've tried to see where they come from,
only after considerable practice with the minutia, gradually adding the trills. Uh,
(20:47):
do we have the full spirit of the idea? Mathematics
like music as a human adventure, people create and discover it,
they try to then share it and enjoy it. Yeah.
I mean I I definitely found that to be the
case with both music and mathematics, because on one hand,
I love um certain genres of music, and I'll you know,
I'll listen to it all the time, but I'm not
(21:07):
necessarily really good at describing what's great about it. Like
if if I'm like, you know, talking to a friend,
I'm like, oh, you gotta listen to this new mix
by so and so, and they might be like, well,
what's awesome about it? And I may be a little
stump for words, you know, unless I have some time
to prep. Likewise, with mathematics, I was the last week
I was working on an article about number theory and
like number theory. Especially when writing for a general audience
(21:30):
and a you know, non math audience, it's it quickly
becomes a conversation that cannot be really held in English
but needs to be held or any language, but needs
to be held in math. You know, it needs to
be held with numerals and and equations. So it becomes
increasingly difficult to to explain the topic without being the
(21:51):
topic right right. And that's why us wildly humans, I suppose,
turned to math and music to try to express ourselves
and our ideas and in a better way. Yeah, because
I think I saw it pointed out that both both
music and math are like they're self describing things. The
music describes itself, the math describes itself, and h and yeah,
at the at the end of the day, it kind
(22:11):
of sounds like, you know, defeatist, but they both kind
of described themselves the best. There we go looking in
the mirror. I'm trying to change the world. I don't
know I was trying to do, Michael Jackson, there apologize
you were trying to do like an impersonation. I was
thinking that math and music we're looking at each other
in the world. And then excuse me, looking at each
(22:33):
other in the mirror, and then I started thinking about
that song man in the mirror. Oh, it's just bad
all around. No, No, it wasn't that bad. It was good.
You did fun um. If we have the speaking of math,
we have a listener mail here, a listener by the
name of Timothy. He says, hello, stuff to all your
mind crew. I just wanted to say thank you for
the unusually deep mathematics podcast. I am a science and
(22:54):
philosophy enthusiast, and I just happened to be in the
middle of a book called A World Without Time, the
Forgotten Legacy of Godal and Einstein when you aired your podcast.
I personally believe that Godal's incompleteness, theorems, the existence of
non eucludean geometries, the necessity of imaginary numbers, and such
all point to math is a formal system invented by humans.
(23:15):
It strikes me as something similar to a game like chess,
where simple rules give rise to an incredibly complex overall system.
I could imagine a chess like game being created to
model physics. What is interesting to me is that Godal,
like many mathematicians, was of the opposite persuasion. He believed
that math exists independent of the human mind. By the way,
(23:36):
one of my favorite books is also godal escher Bach
by Douglas hofstadtur Hofstadter Yeah, can we as ye, which
I highly recommend it to any listeners who also enjoyed
the Math podcast. Thank you for all the hard work
you to do, Tim. Thanks Tim. Yeah, so, yeah, the
we have the podcast that we've in referenced earlier. Um
(23:59):
is math a human invention or a human discovery? And uh, yeah,
that was a lot of fun to do. Yeah it was.
And and uh again, we were both a little bit
trepidacious about, you know, entering into the realm of math,
but it turns out it was not painful at all. Yeah,
And if you want to enter into our realm, then
all you have to do is check out Facebook and Twitter.
It is not painful either, not painful at all. I
(24:21):
mean unless like twitters down or something, and it can
be a little frustrating. But now we'll blow the mind
on both of those and we update that with all
sorts of links to cool stuff. We're reading cool stuff,
we're writing cool stuff that we just podcasts about, and
we would love to hear from you. So Please feel
free to drop us a line at blow the Mind
at how stuff works dot com. Be sure to check
(24:44):
out our new video podcast, Stuff from the Future. Join
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